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Applied Mechanics Projects

If you like making things that move, or taking things apart to see how they work, then this could be a good place to find an idea for your next science fair project. Applied Mechanics takes the laws of classical mechanics and puts them to work solving real-world problems.

• The Physics of Cheating in Baseball
• Effect of Friction on Objects in Motion
• Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance
• Measuring Vibrational Frequency with Light
• Additional Project Ideas

Sorry, no difficulty levels here.

Additional Project Ideas

Additional Project Ideas

• Hey Gear Heads! The Physics of Bicycle Gear Ratios
  If you have a multi-speed bike, you know that you can make it easier or harder to pedal just by shifting gears. Ever wonder how that works? You can investigate this a number of ways. A basic approach is to use a selection of spools of thread (with different diameters), a board with two nails, and a rubber band. Place a spool over each nail, and put the rubber band over them. Mark the 12:00 position on each spool so that you can count revolutions. Turn one spool through a full circle and note how far the second spool turns. Try with different combinations of spool sizes. Explain how your results relate to bicycle gears. You can also do this with a multi-speed bike: turn the bike over, and mark a position on the rear wheel with tape so you can count revolutions. Or, maybe your bike has a speedometer and cadence monitor (this uses magnets on the crank and wheel, and fixed sensors mounted on the frame to count). Have a helper hold the rear wheel up while you move the pedal at a fixed cadence (make sure there is no slack in chain). Record the resulting speeds for each gear combination. Count the teeth on the front sprockets and rear gears. Divide the number of teeth in front by the number in back for each gear combination. Knowing the wheel circumference, you can calculate the wheel's angular speed (revolutions per minute, or rpm's) from the recorded speed. Graph your results. Is there a relationship between the ratio of the gear teeth and wheel rpm's? (Idea from Wiese, 2002, pp. 62–67.)

  Wiese, Jim. Sports Science: 40 Goal-Scoring, High-Flying, Medal-Winning Experiments for Kids. New York: John Wiley and Sons, 2002.

• Air Pressure and Rolling Resistance
  How does the air pressure in a tire affect the rolling resistance of a bicycle or wheelbarrow? Do you need more or less effort to move the bicycle (or wheelbarrow) as the air pressure is changed? Use a tire pressure gauge to monitor air pressure (don't exceed the recommended tire pressure). For the bicyle, you could probably use a spring scale to measure how much force is needed to pull the bicycle along (have a friend lightly touching the bike to keep it balanced). Quantifying the force needed to move the wheelbarrow will be a bit more difficult. You may have to resort to a 1–5 rating scale (e.g., where 1="I can do this all day," 2="takes a bit of effort," 3="a good workout," 4="pushing myself pretty hard," and 5="maximum effort.") For more advanced students, can you explain your results in terms of frictional forces?

• Physics of Vibrations
  Tennis racquets, baseball bats and golf clubs all vibrate when they hit the ball. You can often feel it in your hands, particularly if you "mis-hit" the ball. You can find the point(s) on your racquet, bat or club—called the "sweet spot"— that minimize unwanted vibrations. Low-tech method: hang the racquet or bat straight up and down with a string from its handle. Lightly hold the handle with your thumb and forefinger and have a helper sharply tap the bat, strings or club face with a ball at regular increments along the length. You'll feel a minimum in the vibration at the "sweet spot" of the bat, racquet or club. High-tech method: loosely tape a card to the handle so that it will vibrate when the racquet, bat or club is tapped (Brody, 1987, p. 33). If you want to go all out, you can measure the vibration of the card by monitoring light reflecting off the card with a photodiode and analog-to-digital converter. Several projects possible: longest hit from where? best accuracy from where? comparing different racquets for comfort? (Both Brody et al., 2002, and Brody, 1987, have extensive sections on the vibration of racquets; Barr, 1990, pp. 37–39, has a short treatment of vibration in baseball bats.)
  • Barr, G., 1990. Sports Science for Young People. New York, NY: Dover Publications.
  • Brody, H., 1987. Tennis Science for Tennis Players. Philadelphia, PA: The University of Pennsylvania Press.
  • Brody, H. et al., 2002 The Physics and Technology of Tennis. Solana Beach, CA: Racquet Tech Publishing.

• Skiing and Friction
  How does ski wax affect the sliding friction of skis? You can model this with an ice cube sliding down a plank: how high do you need to lift the end of the plank before the ice cube starts to slide? Try this with one side plain wood and the flip side waxed wood (use paraffin wax, candle wax or ski wax). Make sure both sides are equally smooth to start with. Do at least three trials. More advanced: using what you know about the forces acting on the ice cube, derive equations to calculate the coefficient of friction for each case. Variation: chill the planks to different temperatures (e.g., inside, vs. outside, vs. enclosed, but unheated porch; or use your freezer; make sure the boards stay long enough to reach equilibrium). Do tests at steady temperature, try different cross-country ski waxes at each temperature. (Idea from Wiese, 2002, pp. 54–56.)

  Wiese, Jim. Sports Science: 40 Goal-Scoring, High-Flying, Medal-Winning Experiments for Kids. New York: John Wiley and Sons, 2002.

• The Turn of the Screw
  How much force is required to advance a lag bolt (large wood screw with a hex-shaped head) into a piece of wood? You can measure the force by using a spring scale attached to the handle of ratchet. Pull on the spring scale until the bolt starts to turn, and note the required force from the spring scale. There are many potential experiments you could try. Think about answering the following questions: How does the force change as the bolt advances deeper into the wood? Why? How does the required force change as the diameter of the pilot hole is changed? Why? Can you change the required force by rubbing the bolt's threads with soap or wax? (Coyle, 2005)

  Coyle, C.P., 2005. "Some Variables Affecting the Torque Required to Turn a Screw," California State Science Fair Project Abstract [accessed April 18, 2006] http://www.usc.edu/CSSF/History/2005/Projects/J0205.pdf.

• Effect of Temperature on Elasticity of Rubber Bands
  How much force can a rubber band withstand before breaking? Do rubber bands that stretch longer take more or less force to break? How does the elasticity of a rubber band change with temperature? Use a spring scale to measure the applied force, and a meter stick or ruler to measure the change in length. Recording with a video camera (or possibly two) can help you to capture the values at the moment before the rubber band breaks. You can change the temperature of the rubber bands using heated or cooled water. (Coy, 2005)

  Coy, A.R., 2005. "How Does Temperature Affect a Rubber Band's Elasticity?" California State Science Fair Project Abstract [accessed April 18, 2006] http://www.usc.edu/CSSF/History/2005/Projects/J0204.pdf

• Domino Theory
  Have you ever set up a line of dominoes and watched them fall? If you wanted to make your line of dominoes fall faster, do you think you should set the dominoes up with more or less space between them? Set your dominoes up in a straight line, using a ruler to keep the spacing between them constant. Try different spacings at 0.5 cm increments. Conduct multiple trials at each spacing, and time how long it takes for a fixed total length of dominoes to fall (e.g., a 1.5 or 3.0 meter length of dominoes). Average your results for each spacing. At which spacing do the dominoes fall the fastest? Can you explain your results? Can you predict the optimal spacing for a set of taller (or shorter) dominoes? Find another set and test your prediction! (Gatanaga, D.A., 2004)

  Gatanaga, D.A., 2004. "How Does the Distance Between Dominoes Affect the Speed That Dominoes Fall?" California State Science Fair Project Abstract [accessed April 18, 2006] http://www.usc.edu/CSSF/History/2004/Projects/J0211.pdf

Resources

Sources for Additional Project Ideas

• Coy, A.R., 2005. "How Does Temperature Affect a Rubber Band's Elasticity?" California State Science Fair Project Abstract [accessed April 18, 2006] http://www.usc.edu/CSSF/History/2005/Projects/J0204.pdf.
• Coyle, C.P., 2005. "Some Variables Affecting the Torque Required to Turn a Screw," California State Science Fair Project Abstract [accessed April 18, 2006] http://www.usc.edu/CSSF/History/2005/Projects/J0205.pdf.
• Barr, George. Sports Science for Young People. New York: Dover Publications, 1990.
• Brody, Howard. Tennis Science for Tennis Players. Philadelphia: The University of Pennsylvania Press, 1987.
• Brody, Howard et al. The Physics and Technology of Tennis. Solana Beach, CA: Racquet Tech Publishing, 2002.
• Gatanaga, D.A., 2004. "How Does the Distance Between Dominoes Affect the Speed That Dominoes Fall?" California State Science Fair Project Abstract [accessed April 18, 2006] http://www.usc.edu/CSSF/History/2004/Projects/J0211.pdf.
• Wiese, Jim. Sports Science: 40 Goal-Scoring, High-Flying, Medal-Winning Experiments for Kids. New York: John Wiley and Sons, 2002.

Measuring Vibrational Frequency with Light

Objective

The goal of this project is to measure the vibrational frequency of spring/mass combinations using springs of different stiffness and a graded range of masses for each spring.

Introduction

Have you ever "twanged" a ruler sticking off the edge of a desk and then pulled it back to hear the funny sound it makes? When you twang the ruler, it vibrates at a natural frequency determined by the stiffness of the ruler material and the length of the ruler that is able to vibrate. As you pull back on the ruler, the length that is free to vibrate becomes shorter and shorter. The frequency of the vibration increases, and you hear that funny, rising sound.

Any solid object will have a natural vibration frequency. For massive objects, the vibrations may be very small, and thus hard to measure. In this project, you will measure the vibration frequencies of springs with different masses hanging from them. Try to find a selection of springs with a wide variety of stiffnesses. For each spring, use a range of masses. Be careful not to put too much weight on each spring, though. If you put too much strain on the spring, you will go beyond its range of elasticity and you will end up permanently deforming the spring.

The Experimental Procedure section explains how you can build a simple light-sensor circuit which you can use with an analog-to-digital (A/D) converter to measure the frequency of vibration of your different spring/mass combinations. An A/D converter takes an analog signal (the voltage signal from your light-to-voltage circuit) and converts it to a digital signal (a stream of 0's and 1's, the language of computers). The A/D converter samples the analog signal at regular intervals (called the sampling rate or sampling frequency) and converts the signal to a number that is proportional to the strength of the signal. The sampling rate places a limitation on the frequency of the signals that can be accurately recorded. In theory, you can resolve a signal at half the sampling frequency.

In practice, the sampling rate should be slightly higher than twice the desired maximum frequency. For example, audio signals, which range from 20–20,000 Hz, are sampled at 44,100 Hz for typical MP3 files. For digital TV, and digital audio tape recorders, the sampling rate for audio is even higher, 48,000 Hz.

The inexpensive A/D converter recommended for this project can sample at a maximum rate of 240 Hz, so you the maximum frequency of the signals you can expect to record is about 100–105 Hz.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

• Hooke's law,
• vibrational frequency,
• sampling rate (or sampling frequency).

Questions

• If an A/D converter has a sampling rate of 240 samples per second, what is the maximum frequency that can be reliably detected?

Bibliography

• Wikipedia contributors, 2006. "Hooke's Law," Wikipedia, The Free Encyclopedia [accessed November 16, 2006] http://en.wikipedia.org/w/index.php?title=Hooke%27s_law&oldid=87579136.
• Light-to-Voltage Converter Data Sheet: TAOS, Inc., 2006. "TSL12S, TSL13S, TSL14S Light-to-Voltage Converters," [accessed November 16, 2006] http://www.taosinc.com/images/product/document/TSL12S-E20.pdf.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• light-to-voltage converter (e.g., part number 856-TSL14S-LF, Mouser Electronics),
• 10 kΩ, 1/4-watt resistor (e.g., part number 271-10K-RC, Mouser Electronics),
• 3 AA batteries,
• battery holder (e.g., part number 12BH331-GR, Mouser Electronics),
• insulated connecting wire,
• for building the circuit you can use:
  • solderless breadboard (e.g., part number 517-922306, Mouser Electronics), or
  • you can solder the circuit together and install them in a small enclosure (you'll need to drill a hole and position the sensor so that light can reach it),
• flashlight,
• analog-digital (A/D) converter with data acquisition software (e.g., DI-194RS, DATAQ Instruments),
• computer with serial port,
• springs of different stiffness,
• masses to hang from springs (range of a few grams to kilograms, depends on stiffness of springs).

Disclaimer: Science Buddies occasionally provides information (such as part numbers, supplier names, and supplier weblinks) to assist our users in locating specialty items for individual projects. The information is provided solely as a convenience to our users. We do our best to make sure that part numbers and descriptions are accurate when first listed. However, since part numbers do change as items are obsoleted or improved, please send us an email if you run across any parts that are no longer available. We also do our best to make sure that any listed supplier provides prompt, courteous service. Science Buddies receives no consideration, financial or otherwise, from suppliers for these listings. (The sole exception is the Amazon.com link.) If you have any comments (positive or negative) related to purchases you've made for science fair projects from recommendations on our site, please let us know. Write to us at scibuddy@sciencebuddies.org.

Experimental Procedure

Building the Vibration Frequency Detector Circuit

1. The circuit is very simple. The light-to-voltage converter is an integrated package that contains a photodiode and an amplifier (Figure 1 shows the functional block diagram).

   Figure 1. Light-to-voltage converter functional block diagram. (TAOS, Inc., 2006)

   Light (arrows) illuminates the photodiode sensor and generates a current. The operational amplifier (or "op amp," symbolized by the large triangle in the diagram) produces an output voltage that is proportional to the intensity of the light illuminating the photodiode.
2. A drawing of the actual component is shown in Figure 2. The round window contains the light-sensitve region. The component has three pins, as shown.
   1. Pin 1 should be connected to ground (black wire from the battery holder).
   2. Pin 2 should be connected to the positive supply voltage (red wire from the battery holder). The supply voltage should be between 2.5 and 5.5 V DC, so you can use either 2 or 3 AA batteries.
   3. Pin 3 is the output voltage, a signal that is proportional to the amount of light falling on the sensor.

   Figure 2. Drawing of light-to-voltage converter package. (TAOS, Inc., 2006)

3. Figure 3 shows a schematic diagram of the complete circuit. In addition to the light-to-voltage converter, there is only one more component: a 10 kΩ resistor (R_L). Connect the resistor from pin 3 to ground, as shown.

   Figure 3. Light-to-voltage converter circuit schematic. (TAOS, Inc., 2006)

4. The output signal is the voltage drop across the 10 kΩ resistor. Connect pin 3 to the channel 1 input on the DI-194RS, and connect pin 1 to the GND input on the DI-194RS.
5. You can easily build the circuit on a solderless breadboard.

   Figure 4, below shows a small breadboard. The breadboard has a series of holes, each containing an electrical contact. Holes in the same column (examples highlighted in yellow and green) are electrically connected. When you insert wires into the holes in the same column, the wires are electrically connected. The gap (highlighted in orange) marks a boundary between the electrical connections. A wire inserted in one of the green holes would not be connected to a wire inserted in one of the yellow holes. Integrated circuits, such as the oscillator used in this project, should be inserted so that they span the gap in the breadboard. That way, the top row of pins is connected to one set of holes, and the bottom row of pins is connected to another set of holes. If the integrated circuit was not spanning a gap in the breadboard, the pins from the two rows would be connected together (shorted), and the integrated circuit wouldn't work. Finally, the two single rows of holes at the top and bottom (highlighted in red and blue) are power buses. All of the red holes are electrically connected and all of the blue holes are electrically connected. These come in handy for more complicated circuits with multiple components that need to be connected to the power supply.

   Figure 4. An example of a solderless breadboard. The highlighting shows how the sets of holes are electrically connected. The red and blue rows are power buses. The yellow and green columns are for making connections between components. Integrated circuits are inserted to span the gap (orange) so that the two rows of pins are not connected to each other.

6. Alternatively, if you have experience with a soldering iron, you can make the circuit in a small enclosure. You'll have to drill a hole and position the light-to-voltage converter so that light can reach its sensor.
7. If you have a digital multimeter, you can use it to test your circuit. Connect the multimeter across the 10 kΩ resistor, and set the multimeter to read DC volts (the maximum signal will be about 5 V). When you shine a flashlight on the sensor, your multimeter should read between 3 and 5 V (depending on whether you used 2 or 3 batteries). When you cover the sensor, the multimeter should read close to 0 V.

Measuring Vibration Frequency

1. For measuring the vibration of a spring, you will need a continuous readout of the voltage from your circuit. For this, you will use the analog-to-digital (A/D) converter. If you happen to have access to an oscilloscope, you could use that instead.
2. Follow the instructions that come with the DATAQ A/D converter (DI-194RS) for installing the WinDAQ Lite software. Connect the A/D converter to your computer using the supplied serial port cable. (Be sure to use the thumbscrew connectors to insure a good ground connection.)
3. Connect the A/D converter to read the voltage across the 10 kΩ resistor in your circuit. To do this, connect the ground from your light-to-voltage circuit to the GND connection on the A/D converter, and connect the output (pin 3) to the Channel 1 input on the A/D converter.
4. Start the WinDAQ Lite software.
5. By default, the WinDAQ software will take samples from each of the four input channels, cycling through all four channels before repeating with the first channel. Since you are only using one input channel, you can turn off sampling on channels 2–4.
   1. To turn off sampling on a channel, select Edit/Channels (or press the "F5" function key). Type "-" and then the channel number to turn off sampling for that channel, then hit Enter. Turn off sampling for channels 2, 3, and 4.
   2. This means that the software will only sample from one channel, so the sampling rate will be four times faster. The maximum sampling rate of the DI-194RS is 240 samples/s. When sampling from all four channels, the maximum rate is thus 60 samples/s for each channel. When sampling from a single channel, the maximum rate is 240 samples/s.
   3. Note that the theoretical maximum frequency you can resolve with the DI-194RS when sampling a single channel at the maximum rate is 0.5 × 240 samples/s or 120 Hz. Practically, the maximum frequency will be about 100–105 Hz.
6. The output of the light-to-voltage converter ranges from 0 to about 5 V. The DI-194RS has a fixed gain, so its dynamic range is always -10 to +10 V. However, you can change the scaling of the signal on the screen so that you can see the response more easily. From the menus, select Scaling/Limits, and change the upper and lower limits to 5 and 0V, respectively.
7. You can test to see that the A/D converter is working by pointing a flashlight on the sensor and then away. You should see the voltage rise when the light is on the sensor and then fall when the light moves away. If you don't see a response, go back and check all of your connections and try again.
8. Next you need to hang a spring from a sturdy support and attach a weight to the bottom. Position the sensor behind the weight, right near the top edge. Shine the flashlight directly at the weight. When you pull down on the weight, the light should fall on the sensor. When you let go of the weight, the spring will vibrate, and the weight will move up and down, blocking and unblocking the sensor. From the changing voltage output of your circuit, you will be able to measure the frequency of the vibration.
9. Practice setting the weight vibrating a couple of times to make sure that everything is positioned correctly. The flashlight should be bright enough to provide a full-scale response (i.e., about 5 V) when it falls on the sensor.
10. The A/D converter can record the voltage data to a file, which you can later analyze to measure the vibration frequency.
    1. Select File/Open from the menus.
    2. Type a name for your data file and press . To help you keep track of your data, the name should identify the spring and weight used for each file.
    3. To record, press .
    4. Pull down on the weight and release it to set the spring vibrating.
    5. When the vibrations have stopped, pull down and release the weight again. Record at least 3 trials.
    6. To stop recording, press .
11. Repeat for each spring/mass combination, using a separate file for each one.
12. To measure the frequency of vibration, use the WinDAQ Waveform Browser software to open the data file. Since you have data on only one channel, you should format the screen to view only that channel. Choose View/Format Screen and select "1 Waveform."
13. Figure 5 illustrates some of the features of the software and shows data measured from the spring-loaded plunger on a pinball machine.

    Figure 5. Screenshot of the WinDAQ Waveform Browser software. Data readout line is highlighted in yellow. Click and drag on this line to move the data cursor with the mouse. You can also see the voltage signal increase when the plunger is pulled back, then decrease when the plunger is let go. The three sharp peaks that follow are due to the vibration of the plunger allowing light to pass through to the sensor.

14. You can position the data cursor (Options/Data Cursor) with the arrow keys, or by clicking and dragging in the data read-out line just below the graph. In Figure 6, the data cursor has been dragged to the peak of the first vibration, when the plunger had bounced out of the way and the sensor was receiving the maximum amount of light.

    Figure 6. In this screenshot, the data cursor is now positioned at the first peak. The data readout line shows the time of this peak (since the beginning of the file).

15. Now you can use a Time Marker to measure the time between the data cursor position and the moveable Time Marker. It's a little confusing at first, because the Time Marker looks just like the Data Cursor. You can move it with the arrow keys, or by clicking and dragging in the data readout line. When you enable a Time Marker, the current position of the Data Cursor becomes a blue line. As you drag the Time Marker, the data readout line shows the measured time between the Data Cursor and the Time Marker. See Figure 7.

    Figure 7. In this screenshot, the Time Marker is now enabled. The position of the data cursor is now shown in blue. The Time Marker has been positioned at the second peak, and the time between the two peaks is given on the data readout line (highlighted in yellow).

16. The frequency of the vibrations is the reciprocal of the time between two adjacent peaks. In the case of the pinball plunger spring from Figure 7, the frequency is 1/0.054 s, or 18.5 Hz.
17. Repeat the measurements for each pair of peaks and for all of the trials for each spring/mass combination.
18. For each spring, make a graph of vibration frequency vs. weight.

Variations

• The Wikipedia article on Hooke's Law (Wikipedia, 2006) contains an equation relating frequency of vibration, stiffness of a spring, and mass on the spring. Does this equation fit your results?
• See if you can use the sensor to measure the vibration of a ruler (described in the first paragraph of the Introduction). How does the vibration frequency change as the ruler is shortened? Design an experiment to find out.

Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance

Objective

The goal of this project is to determine how changing the length of throwing arm or the mass of the counterweight will affect the distance that a projectile can be thrown by a trebuchet.

Introduction

A trebuchet is kind of catapult that uses a counterweight to supply the energy for throwing the projectile. They were used as siege engines in the Middle Ages in Europe to hurl heavy stones at castle walls. The power of the trebuchet is based on a simple machine: the lever.

Figure 1, below, is a picture of a reconstructed trebuchet, at Château des Baux, France. The counterweight hangs from the short end of the lever arm, and the projectile is held in a sling attached to the long end of the lever arm. To prepare the trebuchet for firing, the long end of the lever arm is pulled down, which raises the short end of the lever arm, along with the counterweight that hangs from it. The counterweight is much heavier than the projectile, so when the lever arm is let go, the counterweight falls, whipping the long end of the lever arm up into the air. The sling increases the whipping action and hurls the projectile into the air.

Figure 1. Reconstructed trebuchet at Château des Baux, France. The projectile is held in the sling, at the long end of the lever arm (at left). The long end of the lever arm is pulled down, raising the counterweight suspended from the short end of the lever arm (right of center). When the long end of the lever is let go, the counterweight pulls the short end of the lever down, whipping the long end of the lever arm up. The sling follows, and the projectile is sent flying through the air. (Wikipedia, 2006)

As you can see from Figure 1, most of the material that goes into building a trebuchet is used to make a solid supporting structure for the lever, but it is the lever that does the work. Figures 2 and 3, below, strip away the support structure to focus on the trebuchet lever.

Figure 2. Diagram of a trebuchet lever arm. The pivot point is off-center, so a 10 kg counterweight on the short arm just balances a 2 kg projectile on the long arm, at 5× the distance. (Diagram modeled on Gurstelle, 2004, page 144.)

The key to the trebuchet lever arm is the location of the pivot (or fulcrum). The pivot is off-center, with the counterweight suspended from the short arm. Figure 2 shows the trebuchet lever in a balanced condition. A 10 kg counterweight just balances a 2 kg projectile because the projectile is five times further from the pivot point. In actual use, the counterweight would be much heavier than the projectile.

Figure 3 shows what happens when the loaded trebuchet lever is released. The counterweight falls, raising the long end of the lever arm. In this case, the long end of the lever would fly up five times faster than the counterweight falls. The lever provides a mechanical advantage, trading the weight of the falling counterweight for speed of the long lever arm.

Figure 3. Diagram of a trebuchet lever arm in action. The trebuchet uses the mechanical advantage of the lever to trade weight for speed. (Diagram modeled on Gurstelle, 2004, page 144.)

For the army attacking a castle with a trebuchet throwing distance was very important, in order to stay out of range of the defending archers. What lever arm length produces the greatest hurling distance? What is the best weight to use for a particular lever arm and projectile? In this project, you can build a model trebuchet and find out for yourself.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

• catapult,
• trebuchet,
• fulcrum (or pivot),
• lever,
• mechanical advantage.

More advanced students should also study:

• momentum,
• kinetic energy,
• potential energy, and
• Newton's laws of motion.

Questions

• How does placement of the pivot point on the lever arm affect the mechanical advantage of the trebuchet?
• What should the mechanical advantage be for optimal throwing distance?
• What should the mass of the counterweight be for optimal throwing distance?
• What should the length of the sling be for optimal throwing distance?
• How is throwing accuracy affected by the above-mentioned factors?

Bibliography

• A good place to start your research is this Wikipedia article on trebuchets:
  Wikipedia contributoros, 2006. "Trebuchet," Wikipedia, The Free Encyclopedia [accessed November 9, 2006] http://en.wikipedia.org/w/index.php?title=Trebuchet&oldid=87386114.
• The PBS NOVA Online website has an episode on Medieval Sieges that has information on trebuchets. You can play an interactive game to destroy a castle (requires Shockwave) and learn about the mechanics of trebuchets:
  WGBH, 2000. "Secrets of Lost Empires: Medieval Siege," WGBH Educational Foundation [accessed November 9, 2006] http://www.pbs.org/wgbh/nova/lostempires/trebuchet/.
• More advanced students should also study Newton's three laws of motion, which are introduced in these four lessons from The Physics Classroom:
  Henderson, T., 2004. "Newton's Laws," The Physics Classroom and Mathsoft Engineering & Education, Inc. [accessed November 8, 2006] http://www.physicsclassroom.com/Class/newtlaws/newtltoc.html.
• This book has detailed plans for building seven different historic catapult types, as well as information on the history and mechanics of catapults:
  Gurstelle, W., 2004. The Art of the Catapult: Build Greek Ballistae, Roman Onagers, English Trebuchets, and More Ancient Artillery. Chicago, IL: Chicago Review Press, Inc.
• Filip Radlinski did a school physics project based on a trebuchet and put together this excellent website that summarizes his work (includes building tips and photographs):
  Radlinski, F., 1997a. "The Physics of the Trebuchet," Filip Radlinski personal website [accessed November 9, 2006] http://www.geocities.com/SiliconValley/Park/6461/trebuch.html.

Materials and Equipment

There are many trebuchet plans to choose from. The book The Art of the Catapult, by William Gurstelle (Gurstelle, 2004), has several plans. You can also find plans online by doing a web search on 'trebuchet plans.' Here are some things to look for in a good plan:

• appropriate size for your test area ("tabletop" models are probably your best bet unless you have lots of space for testing),
• readily available materials,
• clear illustrations and instructions.

For building the trebuchet, you will need:

• wood,
• fasteners,
• glue,
• sandpaper, and
• tools for cutting the wood to size.

You'll also need:

• a projectile (e.g., practice golf balls or other small, light balls), and
• a tape measure.

Experimental Procedure

Safety note: adult supervision is required for this project. Trebuchets have moving parts and are designed to throw projectiles. Exercise proper caution when building and using your trebuchet.

1. Choose a trebuchet design (see the Materials and Equipment section above, for suggestions).
2. Build your model.
3. Try different lengths for the long end of the lever arm. Remember that you'll need to plan for extra materials in order to build the different lever arms for testing.
4. Try different masses for the counterweight.
5. For each condition, conduct at least 10 trials to test the throwing distance. Measure and record the distance from the trebuchet to where the projectile first lands.
6. Calculate the average distance for each condition. More advanced students should also calculate the standard deviation.
7. Graph your results. Which condition produced the longest throw? Do the data show a consistent trend? Do your data suggest that you could make further increases in throwing distance?

Variations

• Determine the accuracy of your trebuchet. Fire a large number of shots with identical conditions (i.e., same payload, counterweight, lever arm, launch angle). Record where each shot lands (distance and angle from trebuchet). Graph the results. What is the average distance for a shot? What is the scatter? How do distance and scatter change as you systematically vary one shooting parameter (e.g., payload weight, lever arm length, counterweight mass)?
• For another project featuring catapults, see the Science Buddies project Bomb's Away! A Ping Pong Catapult.
• What is the optimal length for the sling that holds the projectile? Design an experiment to find out.
• Compare different trebuchet designs and see if you can determine which feature(s) are important for increasing the distance a projectile can be thrown. Then build two or more trebuchets to compare the feature (or features) you've identified and how it affects performance.

Credits

Andrew Olson, Ph.D., Science Buddies

Sources

This project is based on:

• McGiffen, K.C., 2003. "Investigations into the Art of Hurling: Effects of Trebuchet Arm Length and Counterweight Mass on Projectile Distance," California State Science Fair Project [accessed November 9, 2006] http://www.usc.edu/CSSF/History/2004/Projects/J0220.pdf.